text:
\section*{Abstract}
\else \normalsize
\begin{center}
{\large\bf Abstract\vspace{-.5em}\vspace{0pt}}
\end{center}
\quotation
\fi}
\def\if@twocolumn\else\endquotation\fi{\if@twocolumn\else\endquotation\fi}
\catcode`\@=12

\begin{document}
\baselineskip=.285in

\preprint{SNUTP-96-010}

\title{\Large\bf Lattice Gauge Theory \\ of\\
Three Dimensional Thirring Model
\protect\\[1mm]\ }
\author{\normalsize Seyong Kim\\[2mm]
{\normalsize\it Center for Theoretical Physics, Seoul National University,
Seoul 151-742, Korea}\\[2mm]
{\normalsize\it skim$@$ctp.snu.ac.kr}\\[6mm]
{\normalsize Yoonbai Kim}\\[2mm]
{\normalsize\it Department of Physics, Pusan National University,
Pusan 609-735, Korea}\\[2mm]
{\normalsize\it yoonbai$@$top.phys.pusan.ac.kr}}
\date{}
\maketitle

\begin{center}
{\large\bf Abstract}\\[3mm]
\end{center}
\indent\indent Three dimensional Thirring model with $N$ four-component
Dirac fermions, reformulated as a lattice gauge theory, is studied
by computer simulation.
According to an $8^{3}$ data and preliminary $16^3$ data, chiral symmetry
is found to be spontaneously broken for $N=2,\;4$ and 6.
$N=2$ data exhibits long tail of
the non-vanishing chiral condensate into weak coupling region, and $N=6$
case shows phase separation between the strong coupling region and
the weak coupling region.
Although the comparison between $8^3$ data and $16^3$ data shows large
finite volume effects, an existence of the critical fermion flavor number
$N_{{\rm cr}}$ $(2<N_{{\rm cr}}<6)$ for which the chiral behavior
changes its character, is suggested by the current numerical data.

\vspace{2mm}

\noindent PACS number(s): 11.15.Ha, 11.30.Qc, 11.30.Rd

\newpage

\pagenumbering{arabic}
\thispagestyle{plain}

Thirring model, appeared in the (1+1) dimensional world around forty years
ago, has shed light on understanding various intriguing issues of field
theories, {\it e.g.}, exactly-soluble models, bosonization, conformal
fixed point, etc. Recently, the very model with $N$ four-component Dirac
fermions has attracted attention in the (2+1) dimensional world
with regard to renormalizability of four-fermion models
in the context of $1/N$-expansion \cite{Par}-\cite{Han}, dynamical mass
generation for the fermion in the analysis of Schwinger-Dyson equation
\cite{GMRS}-\cite{Kon} and so on. In the listed works, usually $1/N$ expansion
technique is employed since interesting features of the model are
inherently non-perturbative. In this note, using a Monte Carlo simulation
technique, we consider the Thirring model on
a three-dimensional(3D) cubic lattice, and ask whether the vector-type four
fermion interaction of the model breaks chiral symmetry spontaneously.

The Lagrangian for the 3D Thirring model in
Euclidean space time is given by
\begin{equation}
{\cal L}=\sum_{a}\bar{\psi}_{a}(\gamma_{\mu}\partial_{\mu}+m)\psi_{a}
+\frac{G}{2N}(\sum_{a}\bar{\psi}_{a}\gamma_{\mu}\psi_{a})^{2} .
\end{equation}
Typical way of treating this model is to introduce an auxiliary vector field
$A_{\mu}$ \cite{Par,Han,GMRS,HP,RS}. On a lattice, this leads to an
auxiliary vector field formulation \cite{DH}.
An alternative approach which is attractive to us, is to regard $A_{\mu}$
as a $U(1)$ gauge field. Indeed a reformulation of the Thirring
model as a gauge theory can be achieved through a hidden local
symmetry \cite{BKY}, \cite{KK,IKSY,Kon}:
\begin{equation}\label{HLSac}
{\cal L}_{\rm HLS}=\sum_{a}\bar{\psi}_{a}(\gamma_{\mu}D_{\mu}+m)
\psi_{a}+\frac{1}{2G}(A_{\mu}-\sqrt{N}\partial_{\mu}\phi)^{2},
\end{equation}
where $\psi_{a}$ is a 4-component Dirac spinor, $\phi$ is a fictitious
Nambu-Goldstone boson field (or equivalently a St\"{u}ckelberg field),
and $D_\mu = \partial_\mu - \frac{i}{\sqrt{N}} A_\mu$.

Noticing that the unitary gauge-fixed form of the
above $U(1)$ gauge theory coincides exactly with the original Thirring model,
we expect benefits from gauge-invariant formulation.
One such benefit is that, in the limit of zero bare fermion mass,
one can avoid complications like the dynamical generation of
parity-violating mass \cite{VW} or Chern-Simons term \cite{Red}.
The other is that we have a freedom to choose the most appropriate gauge for
each particular situations of interest, {\it e.g.}, analysis of the
Schwinger-Dyson equation in a rigorous fashion \cite{IKSY} and a
construction of a gauge-invariant effective potential for the chiral
order parameter \cite{Kon}.

Since the model we are considering is free from parity violation
by an exact argument in the gauge theory formulation, we can focus on
the spontaneous breakdown of
chiral symmetry (actually a flavor symmetry breaking
of $U(2N)\rightarrow U(N)\times U(N)$). There are various interesting aspects
to be addressed once the above chiral symmetry breaking occurs,
which were raised by analytic methods. First, a rather systematic
approach of Schwinger-Dyson equations in the gauge theory
formulation \cite{IKSY} suggests a finite, critical number of
the four-component fermion species,
\begin{equation}
N_{\rm cr}=\frac{128}{3\pi^{2}}\approx 4.32\;
\end{equation}
which is obtained in the infinite limit of four-fermion coupling $g$
($g$ is a dimensionless coupling, $G$ rescaled by the ultraviolet
cutoff $\Lambda, g\equiv G\Lambda$).
In contrast, the auxiliary field formulation with the ``{\it Landau
gauge fixing}'' implies otherwise.\footnote{In fact this Landau gauge fixing
amounts to an $R_{\xi}$ gauge in the hidden local symmetry formulation
if we concede that the auxiliary field is a gauge field.}
A crude constant mass approximation to this formulation seems
to predict a chiral symmetry breaking for all $N$ \cite{HP}
\begin{equation}
g_{\rm cr}\propto\exp\Bigl(\frac{\pi^{2}}{16}N\Bigr),
\end{equation}
which also tells us the ratio of the values of the critical coupling
$g_{\rm cr}$ for different $N$'s. Until now, there is no known equivalent
relationship between $g_{\rm cr}$ and $N$ in the gauge theory formulation.
However, if such a relation exists, it should be different from the above
equation since there exists a critical number of fermion flavor $N_{\rm cr}$
in the gauge theory formulation \cite{SSY}.
Second, it may be interesting if we can read the chiral condensate
$\bigl<\bar{\psi}\psi\bigr>$ as a function of the coupling $g$ for
a given $N$. In the gauge theory formulation \cite{Kon}, a critical scaling
behavior was suggested to follow
\begin{equation}\label{psib}
\bigl<\bar{\psi}\psi\bigr>\approx A_{N}\exp\biggl(
-\frac{B_{N}}{\sqrt{\frac{g}{g_{\rm cr}}-1}}\biggr).
\end{equation}
Of course, on a finite lattice, the behavior of the chiral condensate will
be modified by finite volume effect and may be difficult to compare with
this formula away from $g_{\rm cr}$.

Analytic studies in the framework of the Schwinger-Dyson
equations combined with an $1/N$ expansion raised the questions in the above
and it is interesting to investigate these questions by a lattice study.
In choosing an appropriate action for numerical simulation, one can use
an auxiliary vector field formulation without gauge symmetry or employ a gauge
field formulation based on a hidden local symmetry.
Recently simulation results of the auxiliary field formulation case was
reported in Ref.\cite{DH}. Here we adopt the gauge theory formulation and take
advantage of various benefits coming from the gauge theory formulation.
A discretized version of the 3D action, ${\cal L}_{L}$
with a staggered fermion formulation for the fermion part, is
\begin{equation}\label{latac}
{\cal L}_{L}=\sum_{a}{\Phi^{\dagger}}_{a}(M^{\dagger}M)^{-1}\Phi_{a}
-N\beta\sum_{\mu}\cos{(\phi(x+\mu)-\phi(x)+\theta_{\mu}(x))},
\end{equation}
where \(\Phi\) is the pseudo fermion and \(\theta_{\mu}\) is the gauge field,
\begin{equation}\label{mxy}
M_{x,y}=\frac{1}{2}\sum_{\mu}\eta_{\mu}(x)(e^{i\theta_{\mu}(x)}\delta_{y,x+\mu}
-e^{-i\theta_{\mu}(x-\mu)}\delta_{y,x-\mu})+m\delta_{x,y}
\end{equation}
with staggered fermion phase factor, $\eta_\mu (x)$, and
$\beta = 1/g$, after dropping the constant piece. We include a finite
bare fermion mass term and investigate the massless limit by
simulating successively smaller fermion mass, $m$, since our numerical method
prohibits simulating the chiral limit directly. The continuum limit
of this lattice model is free from parity-violating mass or Chern-Simons
term \cite{BB}. The gauge theory formulation of 3D Thirring model
in Eq.(\ref{latac}) looks like 3-dimensional quantum
electrodynamics (QED) + scalar QED with
kinetic term of the gauge field and the Higgs degrees of freedom truncated.
Note that the link variable $\exp(i\theta_{\mu})$ can not be used for the
vector-fermion interaction term, $\bar{\psi}A_{\mu}\gamma_{\mu}\psi$,
in the auxiliary field formulation. This was not encountered in lattice QED3
case because the gauge symmetry fixes uniquely the interaction between
the fermion and the gauge field and it is the same as Eq.(\ref{mxy}).
Since this theory is non-asymptotically free, such differences may lead
to different continuum limits. In addition, since in our gauge field
formulation the gauge kinetic term will be induced
by quantum effects, we can not say whether it will follow compact or
non-compact form yet. Such an effect seems to be realized indeed by
some kind of
discontinuous behavior in the actual simulations for the strong coupling
region \cite{DH}.

Thus far, we have completed simulations for $N=2,\;4$ and 6 systems on a
$8^{3}$ lattice volume with fermion mass, $m=0.05,\;0.025$, and 0.0125 by use
of hybrid Monte Carlo algorithm (HMC). Preliminary data on $16^3$ lattice
for $N = 2$ and 6 will be used for finite volume effect study.
As usual, by defining fermion fields
on even sites only, one can avoid an additional fermion doubling
from $M^{\dagger}M$ and can simulate even $N$ system with this HMC
algorithm \cite{DKK}. For odd $N$'s, we need to use other numerical algorithm
such as hybrid molecular dynamics method \cite{Kim_Kim}.
Typically, we have accumulated \(\tau\sim 10,000\) time unit after discarding
initial \(\tau = 100\) time unit as the equilibration time with
choosing appropriate $\Delta\tau$($= 0.025, 0.02, 0.0125$) which gives
reasonable acceptance rate (50\% to 90\%). The Metropolis step
interval is set to $\tau=0.5$.
As an order parameter for the chiral symmetry, we calculate the chiral
condensate
\begin{equation}
\bigl<\bar{\psi}\psi\bigr> = \bigl< {\rm Tr} M^{-1} \bigr>,
\end{equation}
where we use a single noise vector to estimate the condensate.
In addition, we also calculate internal energy $\bigl<E_\beta\bigr>$ defined
by $\bigl<N\beta (3 - \sum_{\mu}\cos{(\phi(x+\mu)-\phi(x)+\theta_{\mu}(x))})
\bigr>$,
and specific heat $\bigl<{E_\beta}^2\bigr> - \bigl<E_\beta\bigr>^2$ for
each $N$. Mass spectra for the fermion, \(\pi\)(pseudo scalar channel) and
\(\rho\)(vector channel) are also calculated. However, due to a short
extent in the time direction, we were not able to fit the propagators
reliably. Thus, in the following discussion, we will rely mainly on
the chiral condensate measurement.

Qualitative nature of our numerical simulation result can be summarized in
Fig. 1. The figure is the $m \rightarrow 0$ extrapolated chiral
condensate on a $8^3$ lattice volume for $N=2,\;4$, and 6 respectively
as a function of $\beta$,
where we assumed a naive linear behavior in $m$ for the chiral condensate
($\sim c_0 + c_1 m$).
The figure is similar to QED3 case;
in \cite{DKK}, $N = 2$ shows smooth change of the chiral condensate and a
long tail into weak coupling regime, $N = 3$ shows a complex
behavior of the condensate near the critical point, and $N = 5$
shows an abrupt change of the condensate. This supports
the existence of the critical number of fermion flavors for chiral
symmetry breaking in QED3 \cite{ANW}. Likewise, if we believe that the
naive linear extrapolation of the condensate is a correct procedure
in the gauge theory formulation of 3D Thirring model,
there appears
to be a critical $N$ around which the phase transition
changes its character. A complicated second order phase transition
which connects the strong coupling region to the weak coupling region
smoothly ($N=2$) turns into a phase transition
which has a phase separation ($N=6$).

\vspace{4mm}

\setlength{\unitlength}{0.240900pt}
\ifx\plotpoint\undefined\newsavebox{\plotpoint}\fi
\sbox{\plotpoint}{\rule[-0.200pt]{0.400pt}{0.400pt}}%
\begin{picture}(1500,900)(0,0)
\font\gnuplot=cmr10 at 10pt
\gnuplot
\sbox{\plotpoint}{\rule[-0.200pt]{0.400pt}{0.400pt}}%
\put(70,468){\makebox(0,0)[r]{$\bigl<\bar{\psi}\psi\bigr>$}}
\put(820,-50){\makebox(0,0)[r]{$\beta$}}
\put(176.0,169.0){\rule[-0.200pt]{303.534pt}{0.400pt}}
\put(176.0,68.0){\rule[-0.200pt]{0.400pt}{194.888pt}}
\put(176.0,68.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,68){\makebox(0,0)[r]{-0.1}}
\put(1416.0,68.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,169.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,169){\makebox(0,0)[r]{0}}
\put(1416.0,169.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,270.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,270){\makebox(0,0)[r]{0.1}}
\put(1416.0,270.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,371.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,371){\makebox(0,0)[r]{0.2}}
\put(1416.0,371.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,473.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,473){\makebox(0,0)[r]{0.3}}
\put(1416.0,473.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,574.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,574){\makebox(0,0)[r]{0.4}}
\put(1416.0,574.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,675.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,675){\makebox(0,0)[r]{0.5}}
\put(1416.0,675.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,776.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,776){\makebox(0,0)[r]{0.6}}
\put(1416.0,776.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,877.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,877){\makebox(0,0)[r]{0.7}}
\put(1416.0,877.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(176,23){\makebox(0,0){0}}
\put(176.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(309.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(309,23){\makebox(0,0){0.2}}
\put(309.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(441.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(441,23){\makebox(0,0){0.4}}
\put(441.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(574.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(574,23){\makebox(0,0){0.6}}
\put(574.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(707.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(707,23){\makebox(0,0){0.8}}
\put(707.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(839.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(839,23){\makebox(0,0){1}}
\put(839.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(972.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(972,23){\makebox(0,0){1.2}}
\put(972.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1104.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1104,23){\makebox(0,0){1.4}}
\put(1104.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1237.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1237,23){\makebox(0,0){1.6}}
\put(1237.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1370.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1370,23){\makebox(0,0){1.8}}
\put(1370.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(176.0,68.0){\rule[-0.200pt]{303.534pt}{0.400pt}}
\put(1436.0,68.0){\rule[-0.200pt]{0.400pt}{194.888pt}}
\put(176.0,877.0){\rule[-0.200pt]{303.534pt}{0.400pt}}
\put(176.0,68.0){\rule[-0.200pt]{0.400pt}{194.888pt}}
\put(342,793){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(508,764){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(673,634){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(707,568){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(773,448){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(839,313){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(905,229){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(1005,191){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(1038,183){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(1104,176){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(1171,173){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(1337,173){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(342.0,790.0){\rule[-0.200pt]{0.400pt}{1.445pt}}
\put(332.0,790.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(332.0,796.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(508.0,762.0){\rule[-0.200pt]{0.400pt}{1.204pt}}
\put(498.0,762.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(498.0,767.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(673.0,632.0){\rule[-0.200pt]{0.400pt}{1.204pt}}
\put(663.0,632.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(663.0,637.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(707.0,566.0){\rule[-0.200pt]{0.400pt}{1.204pt}}
\put(697.0,566.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(697.0,571.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(773.0,446.0){\rule[-0.200pt]{0.400pt}{0.964pt}}
\put(763.0,446.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(763.0,450.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(839.0,312.0){\rule[-0.200pt]{0.400pt}{0.723pt}}
\put(829.0,312.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(829.0,315.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(905.0,228.0){\rule[-0.200pt]{0.400pt}{0.482pt}}
\put(895.0,228.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(895.0,230.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1005.0,190.0){\rule[-0.200pt]{0.400pt}{0.482pt}}
\put(995.0,190.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(995.0,192.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1038.0,182.0){\rule[-0.200pt]{0.400pt}{0.482pt}}
\put(1028.0,182.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1028.0,184.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1104.0,176.0){\usebox{\plotpoint}}
\put(1094.0,176.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1094.0,177.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1171.0,172.0){\rule[-0.200pt]{0.400pt}{0.482pt}}
\put(1161.0,172.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1161.0,174.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1337.0,172.0){\rule[-0.200pt]{0.400pt}{0.482pt}}
\put(1327.0,172.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1327.0,174.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(229,664){\makebox(0,0){$+$}}
\put(242,671){\makebox(0,0){$+$}}
\put(309,641){\makebox(0,0){$+$}}
\put(342,606){\makebox(0,0){$+$}}
\put(375,526){\makebox(0,0){$+$}}
\put(408,370){\makebox(0,0){$+$}}
\put(441,221){\makebox(0,0){$+$}}
\put(474,184){\makebox(0,0){$+$}}
\put(508,177){\makebox(0,0){$+$}}
\put(541,174){\makebox(0,0){$+$}}
\put(673,171){\makebox(0,0){$+$}}
\put(839,170){\makebox(0,0){$+$}}
\put(1005,170){\makebox(0,0){$+$}}
\put(1171,169){\makebox(0,0){$+$}}

\put(219.00,661.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(219.00,666.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(232.00,668.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(232.00,673.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(299.00,638.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(299.00,643.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(332.00,604.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(332.00,609.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(365.00,524.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(365.00,529.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(398.00,368.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(398.00,372.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(431.00,219.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(431.00,222.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(464.00,183.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(464.00,185.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(498.00,177.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(498.00,178.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(531.00,173.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(531.00,174.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(663.00,170.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(663.00,171.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(829.00,169.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(829.00,170.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(995.00,169.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(995.00,170.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(1161.00,168.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1161.00,169.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\sbox{\plotpoint}{\rule[-0.400pt]{0.800pt}{0.800pt}}%
\put(229,507){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(242,498){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(275,448){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(282,407){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(289,365){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(295,306){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(302,230){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(309,187){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(322,166){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(342,171){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(375,172){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(441,170){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(508,169){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(673,170){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(839,169){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(229.0,504.0){\rule[-0.400pt]{0.800pt}{1.204pt}}
\put(219.0,504.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(219.0,509.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(242.0,495.0){\rule[-0.400pt]{0.800pt}{1.204pt}}
\put(232.0,495.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(232.0,500.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(275.0,446.0){\rule[-0.400pt]{0.800pt}{0.964pt}}
\put(265.0,446.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(265.0,450.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(282.0,405.0){\rule[-0.400pt]{0.800pt}{0.964pt}}
\put(272.0,405.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(272.0,409.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(289.0,363.0){\rule[-0.400pt]{0.800pt}{0.964pt}}
\put(279.0,363.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(279.0,367.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(295.0,304.0){\rule[-0.400pt]{0.800pt}{0.964pt}}
\put(285.0,304.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(285.0,308.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(302.0,229.0){\usebox{\plotpoint}}
\put(292.0,229.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(292.0,232.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(309.0,186.0){\usebox{\plotpoint}}
\put(299.0,186.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(299.0,188.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(322.0,165.0){\usebox{\plotpoint}}
\put(312.0,165.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(312.0,167.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(342.0,170.0){\usebox{\plotpoint}}
\put(332.0,170.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(332.0,171.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(375.0,171.0){\usebox{\plotpoint}}
\put(365.0,171.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(365.0,173.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(441.0,169.0){\usebox{\plotpoint}}
\put(431.0,169.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(431.0,170.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(508.0,169.0){\usebox{\plotpoint}}
\put(498.0,169.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(498.0,170.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(673.0,170.0){\usebox{\plotpoint}}
\put(663.0,170.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(663.0,171.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(839.0,169.0){\usebox{\plotpoint}}
\put(829.0,169.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(829.0,170.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\end{picture}
\vspace{4mm}

Figure 1: The chiral condensate, $\bigl<\bar{\psi}\psi\bigr>_{m\rightarrow
0}$, vs. $\beta$
for $N=2$ ($\Diamond$ points), $N=4$ ($+$ points), and $N=6$ ($\Box$ points)
on a $8^3$ lattice.
\vspace{4mm}

\setlength{\unitlength}{0.240900pt}
\ifx\plotpoint\undefined\newsavebox{\plotpoint}\fi
\sbox{\plotpoint}{\rule[-0.200pt]{0.400pt}{0.400pt}}%
\begin{picture}(1500,900)(0,0)
\font\gnuplot=cmr10 at 10pt
\gnuplot
\sbox{\plotpoint}{\rule[-0.200pt]{0.400pt}{0.400pt}}%
\put(60,468){\makebox(0,0)[r]{$\beta^{2}\bigl<\bar{\psi}\psi\bigr>$}}
\put(820,-50){\makebox(0,0)[r]{$\beta$}}
\put(176.0,68.0){\rule[-0.200pt]{303.534pt}{0.400pt}}
\put(176.0,68.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,68){\makebox(0,0)[r]{0}}
\put(1416.0,68.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,203.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,203){\makebox(0,0)[r]{0.05}}
\put(1416.0,203.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,338.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,338){\makebox(0,0)[r]{0.1}}
\put(1416.0,338.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,472.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,472){\makebox(0,0)[r]{0.15}}
\put(1416.0,472.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,607.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,607){\makebox(0,0)[r]{0.2}}
\put(1416.0,607.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,742.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,742){\makebox(0,0)[r]{0.25}}
\put(1416.0,742.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,877.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,877){\makebox(0,0)[r]{0.3}}
\put(1416.0,877.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(291.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(291,23){\makebox(0,0){0.8}}
\put(291.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(520.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(520,23){\makebox(0,0){1}}
\put(520.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(749.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(749,23){\makebox(0,0){1.2}}
\put(749.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(978.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(978,23){\makebox(0,0){1.4}}
\put(978.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1207.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1207,23){\makebox(0,0){1.6}}
\put(1207.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1436.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1436,23){\makebox(0,0){1.8}}
\put(1436.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(176.0,68.0){\rule[-0.200pt]{303.534pt}{0.400pt}}
\put(1436.0,68.0){\rule[-0.200pt]{0.400pt}{194.888pt}}
\put(176.0,877.0){\rule[-0.200pt]{303.534pt}{0.400pt}}
\put(176.0,68.0){\rule[-0.200pt]{0.400pt}{194.888pt}}
\put(233,766){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(291,749){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(405,671){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(520,452){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(634,261){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(806,160){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(863,129){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(978,106){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(1092,90){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(1379,100){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(233.0,762.0){\rule[-0.200pt]{0.400pt}{1.686pt}}
\put(223.0,762.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(223.0,769.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(291.0,745.0){\rule[-0.200pt]{0.400pt}{1.927pt}}
\put(281.0,745.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(281.0,753.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(405.0,666.0){\rule[-0.200pt]{0.400pt}{2.168pt}}
\put(395.0,666.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(395.0,675.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(520.0,448.0){\rule[-0.200pt]{0.400pt}{2.168pt}}
\put(510.0,448.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(510.0,457.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(634.0,257.0){\rule[-0.200pt]{0.400pt}{2.168pt}}
\put(624.0,257.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(624.0,266.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(806.0,156.0){\rule[-0.200pt]{0.400pt}{1.927pt}}
\put(796.0,156.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(796.0,164.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(863.0,125.0){\rule[-0.200pt]{0.400pt}{1.927pt}}
\put(853.0,125.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(853.0,133.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(978.0,102.0){\rule[-0.200pt]{0.400pt}{1.927pt}}
\put(968.0,102.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(968.0,110.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1092.0,86.0){\rule[-0.200pt]{0.400pt}{1.927pt}}
\put(1082.0,86.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1082.0,94.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1379.0,95.0){\rule[-0.200pt]{0.400pt}{2.168pt}}
\put(1369.0,95.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1369.0,104.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\end{picture}
\vspace{4mm}

Figure 2: $\beta^{2}\bigl<\bar{\psi}\psi\bigr>_{m\rightarrow 0}$ vs. $\beta$
for $N=2$ on a $8^3$ lattice.

To elucidate these behaviors
more clearly, in Fig. 2, we search for a continuum scaling window
for $N=2$. Like QED3 $N=0$ and $1$ case, the chiral condensate exhibits a long
plateau in weak coupling region. On the other hand, $N=4$ shows two slopes
and hints flat region.

\vspace{7mm}

\setlength{\unitlength}{0.240900pt}
\ifx\plotpoint\undefined\newsavebox{\plotpoint}\fi
\begin{picture}(1500,900)(0,0)
\font\gnuplot=cmr10 at 10pt
\gnuplot
\sbox{\plotpoint}{\rule[-0.200pt]{0.400pt}{0.400pt}}%
\put(70,468){\makebox(0,0)[r]{$\bigl<\bar{\psi}\psi\bigr>^{2}$}}
\put(820,-50){\makebox(0,0)[r]{$\beta$}}
\put(176.0,158.0){\rule[-0.200pt]{303.534pt}{0.400pt}}
\put(176.0,68.0){\rule[-0.200pt]{0.400pt}{194.888pt}}
\put(176.0,68.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,68){\makebox(0,0)[r]{-0.05}}
\put(1416.0,68.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,158.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,158){\makebox(0,0)[r]{0}}
\put(1416.0,158.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,248.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,248){\makebox(0,0)[r]{0.05}}
\put(1416.0,248.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,338.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,338){\makebox(0,0)[r]{0.1}}
\put(1416.0,338.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,428.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,428){\makebox(0,0)[r]{0.15}}
\put(1416.0,428.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,517.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,517){\makebox(0,0)[r]{0.2}}
\put(1416.0,517.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,607.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,607){\makebox(0,0)[r]{0.25}}
\put(1416.0,607.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,697.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,697){\makebox(0,0)[r]{0.3}}
\put(1416.0,697.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,787.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,787){\makebox(0,0)[r]{0.35}}
\put(1416.0,787.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,877.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(154,877){\makebox(0,0)[r]{0.4}}
\put(1416.0,877.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(176.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(176,23){\makebox(0,0){0}}
\put(176.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(316.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(316,23){\makebox(0,0){0.2}}
\put(316.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(456.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(456,23){\makebox(0,0){0.4}}
\put(456.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(596.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(596,23){\makebox(0,0){0.6}}
\put(596.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(736.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(736,23){\makebox(0,0){0.8}}
\put(736.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(876.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(876,23){\makebox(0,0){1}}
\put(876.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1016.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1016,23){\makebox(0,0){1.2}}
\put(1016.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1156.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1156,23){\makebox(0,0){1.4}}
\put(1156.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1296.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1296,23){\makebox(0,0){1.6}}
\put(1296.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1436.0,68.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(1436,23){\makebox(0,0){1.8}}
\put(1436.0,857.0){\rule[-0.200pt]{0.400pt}{4.818pt}}
\put(176.0,68.0){\rule[-0.200pt]{303.534pt}{0.400pt}}
\put(1436.0,68.0){\rule[-0.200pt]{0.400pt}{194.888pt}}
\put(176.0,877.0){\rule[-0.200pt]{303.534pt}{0.400pt}}
\put(176.0,68.0){\rule[-0.200pt]{0.400pt}{194.888pt}}
\put(351,842){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(526,781){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(701,538){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(736,438){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(806,295){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(876,194){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(946,164){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(1051,159){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(1086,158){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(1156,158){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(1226,158){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(1401,158){\raisebox{-.8pt}{\makebox(0,0){$\Diamond$}}}
\put(351.0,836.0){\rule[-0.200pt]{0.400pt}{2.891pt}}
\put(341.0,836.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(341.0,848.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(526.0,775.0){\rule[-0.200pt]{0.400pt}{2.891pt}}
\put(516.0,775.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(516.0,787.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(701.0,534.0){\rule[-0.200pt]{0.400pt}{1.927pt}}
\put(691.0,534.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(691.0,542.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(736.0,435.0){\rule[-0.200pt]{0.400pt}{1.445pt}}
\put(726.0,435.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(726.0,441.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(806.0,293.0){\rule[-0.200pt]{0.400pt}{0.964pt}}
\put(796.0,293.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(796.0,297.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(876.0,194.0){\usebox{\plotpoint}}
\put(866.0,194.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(866.0,195.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(946,164){\usebox{\plotpoint}}
\put(936.0,164.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(936.0,164.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1051,159){\usebox{\plotpoint}}
\put(1041.0,159.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1041.0,159.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1086,158){\usebox{\plotpoint}}
\put(1076.0,158.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1076.0,158.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1156,158){\usebox{\plotpoint}}
\put(1146.0,158.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1146.0,158.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1226,158){\usebox{\plotpoint}}
\put(1216.0,158.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1216.0,158.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1401,158){\usebox{\plotpoint}}
\put(1391.0,158.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1391.0,158.0){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(232,588){\makebox(0,0){$+$}}
\put(246,600){\makebox(0,0){$+$}}
\put(316,549){\makebox(0,0){$+$}}
\put(351,494){\makebox(0,0){$+$}}
\put(386,382){\makebox(0,0){$+$}}
\put(421,229){\makebox(0,0){$+$}}
\put(456,163){\makebox(0,0){$+$}}
\put(491,158){\makebox(0,0){$+$}}
\put(526,158){\makebox(0,0){$+$}}
\put(561,158){\makebox(0,0){$+$}}
\put(701,158){\makebox(0,0){$+$}}
\put(876,158){\makebox(0,0){$+$}}
\put(1051,158){\makebox(0,0){$+$}}
\put(1226,158){\makebox(0,0){$+$}}

\put(222.00,583.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(222.00,592.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(236.00,595.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(236.00,605.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(306.00,544.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(306.00,553.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(341.00,490.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(341.00,498.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(376.00,380.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(376.00,385.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(411.00,227.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(411.00,230.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(446.00,162.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(446.00,163.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(481.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(481.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(516.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(516.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(551.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(551.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(691.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(691.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(866.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(866.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(1041.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1041.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\put(1216.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}
\put(1216.00,158.00){\rule[-0.200pt]{4.818pt}{0.400pt}}

\sbox{\plotpoint}{\rule[-0.400pt]{0.800pt}{0.800pt}}%
\put(232,358){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(246,347){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(281,294){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(288,257){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(295,225){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(302,191){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(309,164){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(316,158){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(330,158){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(351,158){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(386,158){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(456,158){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(526,158){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(701,158){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(876,158){\raisebox{-.8pt}{\makebox(0,0){$\Box$}}}
\put(232.0,356.0){\rule[-0.400pt]{0.800pt}{1.204pt}}
\put(222.0,356.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(222.0,361.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(246.0,345.0){\rule[-0.400pt]{0.800pt}{1.204pt}}
\put(236.0,345.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(236.0,350.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(281.0,292.0){\rule[-0.400pt]{0.800pt}{0.964pt}}
\put(271.0,292.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(271.0,296.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(288.0,255.0){\rule[-0.400pt]{0.800pt}{0.964pt}}
\put(278.0,255.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(278.0,259.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(295.0,224.0){\usebox{\plotpoint}}
\put(285.0,224.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(285.0,227.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(302.0,190.0){\usebox{\plotpoint}}
\put(292.0,190.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(292.0,192.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(309.0,164.0){\usebox{\plotpoint}}
\put(299.0,164.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(299.0,165.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(316.0,158.0){\usebox{\plotpoint}}
\put(306.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(306.0,159.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(330,158){\usebox{\plotpoint}}
\put(320.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(320.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(351,158){\usebox{\plotpoint}}
\put(341.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(341.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(386,158){\usebox{\plotpoint}}
\put(376.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(376.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(456,158){\usebox{\plotpoint}}
\put(446.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(446.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(526,158){\usebox{\plotpoint}}
\put(516.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(516.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(701,158){\usebox{\plotpoint}}
\put(691.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(691.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(876,158){\usebox{\plotpoint}}
\put(866.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\put(866.0,158.0){\rule[-0.400pt]{4.818pt}{0.800pt}}
\end{picture}
\vspace{6mm}

Figure 3: $\bigl<\bar{\psi}\psi\bigr>^2_{m\rightarrow 0}$ vs. $\beta$
for $N=2$($\Diamond$), $N=4$($+$), and $N=6$($\Box$) on a $8^3$ lattice.
\vspace{6mm}

In Fig. 3, we plot $\bigl<\bar{\psi}\psi\bigr>^2_{m\rightarrow 0}$ vs. $\beta$,
in order to see whether the critical behavior follows a mean field theory,
\begin{equation}
\bigl<\bar{\psi}\psi\bigr> \sim (\beta_c - \beta)^\frac{1}{2}.
\end{equation}
It appears that $N = 2$ data does not agree with a mean field behavior
and $N = 6$ data seems to follow a mean field expectation.
For $N = 4$ data, it is very hard to say whether the system behaves in one way
or the other. From internal energy density and specific heat peak, we obtain
$\beta_c = 0.9(1)$ for $N = 2$, $0.35(5)$ for $N = 4$, and
$0.18(1)$ for $N = 6$. These values are roughly consistent with those obtained
from Fig. 1, 2, and 3.

According to the QED3 case, large finite volume effect is expected
\cite{DKK,HK}. In order to purchase this effect, simulations on larger
lattices and smaller $m$ values are needed. Thus, we are investigating the
same system on a $16^3$ lattice with the masses $m = 0.05, 0.025$ and $0.0125$.
In Table 1, we compare $\bigl<\bar{\psi}\psi\bigr>_{m\rightarrow 0}$ for $N=2$
and in Table 2 compare that for $N=6$ on $8^4$ and $16^3$ volume. The first
column is the chiral condensate for $8^3$ using a linear extrapolation of
all range of $m$ data, the second column is that for $16^3$ using a linear
extrapolation of smaller $m$ data ($m = 0.025,\;0.0125$), and the third
column is that for $16^3$ using a quadratic fit to existing data.
Although the dependence of the chiral condensate on both the size of
lattices and the extrapolation method are considerable quantitatively
(particularly in the very weak coupling region of $N=2$ case),
we found that the overall qualitative nature of the chiral condensate does
not seem to be changed: In all three cases, $N=6$ data are compatible with
mean-field behavior but $N=2$ data is not.

\vspace{2mm}

\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
$\hspace{7mm}\beta\hspace{7mm}$&$\bigl<\bar{\psi}\psi\bigr> (8^3)$
		&$\bigl<\bar{\psi}\psi\bigr> (16^3)$
		&$\bigl<\bar{\psi}\psi\bigr>_{quad} (16^3)$ \\
\hline
0.5    & 0.589(3) & 0.641(9) & 0.643  \\
0.75   & 0.460(2) & 0.493(8) & 0.488  \\
1.0    & 0.142(2) & 0.207(4) & 0.195  \\
1.25   & 0.0218(9)& 0.053(2) & 0.048  \\
1.3    & 0.0134(8)& 0.019(2) & 0.007  \\
1.4    & 0.0071(7)& 0.003(2) &-0.009  \\
\hline
\end{tabular}

\vspace{4mm}
Table 1: Comparison of the chiral condensate for $N=2$

\vspace{5mm}

\begin{tabular}{|c|c|c|c|}
\hline
$\hspace{7mm}\beta\hspace{7mm}$ &$\bigl<\bar{\psi}\psi\bigr> (8^3)$
		&$\bigl<\bar{\psi}\psi\bigr> (16^3)$
		&$\bigl<\bar{\psi}\psi\bigr>_{quad} (16^3)$ \\
\hline
0.18   & 0.135(2) & 0.263(4) & 0.239  \\
0.2    & 0.017(1) & 0.085(2) & 0.058  \\
0.22   &-0.004(1) & 0.031(2) & 0.017  \\
0.25   & 0.0014(8)& 0.004(9) &-0.003  \\
0.3    & 0.0027(7)&-0.028(1) &-0.010  \\
0.35   &          & 0.004(1) & 0.003  \\
0.4    & 0.0004(6)& 0.0004(8)&-0.003  \\
0.45   &          & 0.0006(10)&-0.001 \\
0.5    & 0.0002(5)& 0.0005(7)&-0.001  \\
\hline
\end{tabular}

\vspace{4mm}
Table 2: Comparison of the chiral condensate for $N=6$
\end{center}

In conclusion, we have found spontaneous chiral symmetry breaking
for $N = 2, \;4$ and 6 in 3D Thirring model by use of Monte Carlo
simulation on a $8^3$ and a $16^3$ lattice. However, the chiral condensate in
the $m \rightarrow 0$ limit suggests that the nature of the phase
transition in $N = 2$ is different from that in $N = 6$. $N = 2$ case
has a long tail of non-vanishing chiral condensate in weak coupling region
and $N = 6$ case has a phase separation between the strong coupling
region and the weak coupling region. It suggests a possibility that there
exists $N_{\rm cr}$ where the chiral phase transition becomes
a mean field type transition. This situation is quite similar to
QED3. In contrast to the lattice simulation result of the auxiliary vector
field formulation, our result seems to be more consistent with the gauge
theory formulation of 3D Thirring model in continuum.

For a future work, we think
that further detailed study on finite volume effects is needed
although we have discussed our preliminary data on a $16^3$ lattice.
Also, two further questions remain open: One is whether lattice 3D Thirring
model is similar to 3D lattice QED. The other is whether the induced gauge
field kinetic term takes the form of compact QED-like or noncompact QED-like.
The latter issue will be determined by the importance of topological sector.
At this moment, we do not know what the induced term looks like.

\vspace{7mm}

We would like to thank Ph. de Forcrand, D.K. Hong, J.B. Kogut, P. Maris,
D.K. Sinclair, H.S. Song
and K. Yamawaki for various comments and discussions. S. Ohta and the
Computing Center of the Institute of Physical and Chemical
Research (RIKEN) are acknowledged for their support and allowing us
to access their Fujitsu VPP-500.
This work was supported by the KOSEF(through CTP,
Brain Pool Program and 95-0702-04-01-3) and the Korean Ministry of Education
(BSRI-95-2413).

\def\hebibliography#1{\begin{center}\subsection*{References
}\end{center}\list
  {[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}
\leftmargin\labelwidth	  \advance\leftmargin\labelsep
    \usecounter{enumi}}
    \def\hskip .11em plus .33em minus .07em{\hskip .11em plus .33em minus .07em}
    \sloppy\clubpenalty4000\widowpenalty4000
    \sfcode`\.=1000\relax}

\let\endhebibliography=\endlist

\begin{hebibliography}{100}
\bibitem{Par} G. Parisi, Nucl. Phys. B {\bf 100}, 368 (1975); S. Hikami
and T. Muta, Prog. Theor. Phys. {\bf 57}, 785 (1977); Z. Yang, Texas
preprint UTTG-40-90 (unpublished).
\bibitem{KK} N.V. Krasnikov and A.B. Kyatkin, Mod. Phys. Lett. A {\bf 6},
1315 (1991).
\bibitem{Han} S. Hands, Phys. Rev. D {\bf 51}, 5816 (1995).
\bibitem{GMRS} M. Gomes, R.S. Mendes, R.F. Ribeiro and A.J. da Silva,
Phys. Rev. D {\bf 43}, 3516 (1991).
\bibitem{HP} D.K. Hong and S.H. Park, Phys. Rev. D {\bf 49}, 5507 (1994).
\bibitem{HLY} S.J. Hyun, G.H. Lee and J.H. Yee, Phys. Rev. D {\bf 50},
6542 (1994); Y.M. Ahn, B.K. Chung, J.-M. Chung and Q-H. Park, Kyung Hee Preprint
KHTP-94-05 (unpublished).
\bibitem{RS} G. Rossini and F.A. Schaposnik, Phys. Lett. B {\bf 338},
465 (1994).
\bibitem{IKSY} T. Itoh, M. Sugiura, Y. Kim and K. Yamawaki, Prog. Theor.
Phys. {\bf 93}, 417 (1995).
\bibitem{Kon} K.-I. Kondo, Nucl. Phys. B {\bf 450}, 251 (1995).
\bibitem{DH} L.D. Debbio and S. Hands, Preprint SWAT/95/93, hep-lat/9512013.
\bibitem{BKY} M. Bando, T. Kugo and K. Yamawaki, Phys. Rep. {\bf 164},
217 (1988).
\bibitem{VW} With $N$ four-component fermions in (2+1)D, parity-violating
mass $\bigl<\bar{\psi}i\gamma^{0}\gamma^{1}\gamma^{2}\psi\bigr>$ can be generated
dynamically, however, in this gauge invariant formulation
of the Thirring model, such symmetry breaking is proven to be energetically
unfavorable by using exact argument in C. Vafa and E. Witten, Commun. Math.
Phys. {\bf 95}, 257 (1984) (see Ref.\cite{IKSY}).
\bibitem{Red} Similarly, only under the guardianship of gauge symmetry,
we can clarify this issue as shown in \cite{IKSY}: One can take the
regularization to keep
both $U(1)$ gauge symmetry and parity without any ambiguity for the
four Dirac-fermion case (equivalent to even-number two-component
Dirac-fermions), however the Chern-Simons term identified as the
parity-violating anomaly should arise in odd-number two-component
Dirac-fermion case as in 3D quantum electrodynamics (QED3).
\bibitem{SSY} A. Shibata, M. Sugiura and K. Yamawaki, in preparation.
\bibitem{BB} C. Burden and A.N. Burkitt, Europhys. Lett., {\bf 3}, 545 (1987).
\bibitem{Kim_Kim} S. Kim and Y. Kim, work in progress.
\bibitem{DKK} E. Dagotto, A. Koci\'c and J.B. Kogut, Phys. Rev.
Lett.  {\bf 62}, 1083 (1989); E. Dagotto, J.B. Kogut and A. Koci\'c,
Nucl. Phys. B {\bf 334}, 279 (1990).
\bibitem{ANW} T.W. Appelquist, D. Nash and L.C.R. Wijewardhana, Phys. Rev.
Lett. {\bf 60}, 2575 (1988); T. Matsuki, L. Miao and K.S. Viswanathan, Simon
Fraser University preprint; For a review, see C.D. Roberts and A.G. Williams,
Prog. Part. Nucl. Phys. {\bf 33}, 477 (1994).
\bibitem{HK} S. Hands and J.B. Kogut, Nucl. Phys. B {\bf 335}, 455 (1990).
\end{hebibliography}
\end{document}

redpajama_set_name: RedPajamaArXiv


text:
Colton Herta and Gainbridge Extend with Andretti Autosport through 2027
KULR Technology Group Returns to Andretti Autosport for Indianapolis 500 with Marco Andretti
Andretti Autosport Completes Penultimate INDYCAR Race at Portland International Raceway
Andretti Autosport Faces Fierce Fight in Nashville
No. 98 KULR Livery Unveil
No. 27 INDYCAR Livery Reveal
ROMAIN GROSJEAN JOINS ANDRETTI AUTOSPORT
ALL ACCESS: NICK ALLEN
RECAP: MOTEGI iRACING
MARCO ANDRETTI SET TO SHIFT GEARS
Photographer: SPACESUIT MEDIA
2020 Indianapolis 500 Pole Sitter to refocus racing career, stepping away from full-time INDYCAR competition for the 2021 NTT INDYCAR SERIES season
Third-generation racer set to return to IMS for 105th Running of Indianapolis 500-Mile Race
Marco Andretti to assist Andretti Autosport with pre-season testing and development, including Jan. 19 Sebring test day
STATEMENT FROM MICHAEL ANDRETTI:
"Marco and I have discussed this at length. I both support and respect his decision to take a focus on other areas of life, and maybe even other forms of motorsport. We were working on a full-season INDYCAR entry for him, but he decided he wanted to take a different direction and I respect him for making that decision.
"I think for any multi-generational athlete, it can be really challenging to find your own ground and make your own name on top of your family's. Marco has always had the courage to chart his own path and I'm proud of the career he's built for himself and the person he's become. I know this decision wasn't easy.
"But, like he has said, this is not retirement. He has some great accomplishments behind him and I think he still has many more ahead of him. He's offered to help us out with some testing, I'm looking forward to having him back with us for the 500, and hopefully maybe a few more races through the season."
STATEMENT FROM MARCO ANDRETTI:
"Upon careful thought over the past couple of months, I have made the decision to make some changes to my racing activities and focus for 2021. I recently shared this decision and the changes that I want to make with my Dad and have spoken at length with him about it. I appreciate his openness and for allowing me the flexibility to map out my own course going forward.
"I am fortunate to be in a position at Andretti Autosport to run the full INDYCAR season if I want to. But, instead, I have decided to change up my direction somewhat – to reset – to do something a little different - look at everything fresh and see where that takes me. And, to me, now seems like the appropriate time to do that.
"I definitely am going to keep driving. I still have a deep passion for it and have unfinished business to take care of and some boxes that I want to check before I consider retiring as a driver.
"First and foremost, I remain very hungry to win the Indy 500. It is our biggest stage and the place that I feel I bring the most to the table as a driver. I've come close there and am in the mix there it seems each year. Winning the pole there last year was awesome but that isn't enough - I know that a victory there is in my future so we'll try to get that done in the coming years. As such, I have committed to and am looking forward to running the Indy 500 with Andretti Autosport this year. In addition to being squarely focused on the Indy 500, I might also take a look at running some other races on the INDYCAR schedule as the season progresses, in order to remain "car fit." I have also offered to help the team with some testing and other activities along the way. And, I may look at different opportunities in all of motorsports.
"My involvement in my Andretti Autosport entry will continue.
"I also want to do some sports car racing - maybe even get the chance to do IMSA events with my cousin Jarett, which would be a lot of fun for me. I'll be looking into other sports car opportunities as well in the coming months and welcome discussions in that regard. Marquee events like the 24 Hours of Daytona, 12 Hours of Sebring, and Le Mans would be on that list for sure.
"I am excited for what the future holds for me both on and off the track and, again, am grateful to Dad and Andretti Autosport for allowing me the freedom to change things around as I'd like and to proceed forward a little differently this upcoming season."

redpajama_set_name: RedPajamaCommonCrawl


text:
Articles / Photographer Interviews
Exclusive Interview with Graeme Williams
Posted on October 15, 2019 - By Graeme Williams
Graeme William's work on South Africa is acclaimed worldwide and has been published on the cover of Time magazine twice as well as published in The New York Times Magazine, National Geographic, Newsweek, Stern... to name just a few. But for the last five years he shifted his attention from South Africa to the United States. We asked him a few questions about his new project America Revisited:
Thank you very much Graeme for allowing us to discover your beautiful work.
All About Photo: You came to the US in 2016 for a residency at Ampersand Foundation. How did you land up in Harrisburg, Pennsylvania and what were you looking for photographically? Where you disappointed?
Graeme Williams: No, I definitely wasn't disappointed. I was initially based in New York, and I felt like a kid let loose in a giant toy store. After a week visiting every gallery and museum that I could find, I hired a beaten-up rental car and went in search of an 'average' USA town. Just remembering to drive on the right-hand side of the road was a challenge, so I didn't focus too much on my destination. Harrisburg was where I found myself on the first evening and I landed up staying in the local Red Roof Inn for a few weeks. South Africa has the highest Gini coefficient in the world, meaning that it has the highest income inequality in the world. I was therefore interested in exploring the differences between the poor and high-income communities within Harrisburg and how the economic divide compares with that in South African. No doubt, being poor is grim wherever you live in the world, but the definition of 'poverty' varies widely. In Southern Africa, many families survive on less than US$ 100 per month. I found that most of the people I met, whatever their economic status, were really open and accommodating of me and my camera. I was introduced to a woman called Wanda, who became my guide. She was great and took no trouble from anyone, including me. She would walk up to gangsters and drug dealers and be really bossy, saying things like, 'Hey, this guy is from South Africa, so stand there and let him take your picture.' I put the work together in a book called, Diverging Dreamlines, which was chosen as one of four Best of Show in the annual photobook exhibition at the Davis Orton Gallery/ Griffin Museum of Photography.
Yuma, Arizona. From the series, America Revisited 2019, © Graeme Williams
Mineral Wells, Texas. From the series, America Revisited 2019, © Graeme Williams
When did you decide to come back and why?
I knew back in 2016, that I was going to return to the US to work on an essay that reflected a broader, more personal response to the country.
Is America Revisited finished or do you plan on coming back?
No, the project is definitely not finished. I needed to develop the project to a point at which the images held together as a distinct body of work that hopefully has something to say. It is a lot more difficult to convey a concept or idea for a personal essay compared to say, a journalistic project. A proposal such as 'The effects of climate change on a community hit by drought,' is a lot more accessible than something like, 'I am a South African who is going to photograph the USA in a personal manner.' Having produced this initial set of images, I hope to raise interest and funding to develop the project into something broader and more representative of the country as a whole.
Las Vegas, Nevada. From the series, America Revisited 2019, © Graeme Williams
How did you prepare for this trip?
Usually with long-term projects one has the luxury of letting an idea or concept develop over time. With the weak South African Rand (US$ 1 =15 SAR), I realised that I needed to hit the ground running, so planning became an important aspect of the America Revisited project. It took almost three years to distil what I wanted to say, the feel of the images and how the images should work together as an essay. I found that Google Street View was an amazing tool for getting a clear picture of what things look like on the ground. I find it very disorientating when my preconceptions are way different from reality. I land up spending too much time thinking and recalibrating, instead of just looking in uncomplicated manner.
How long did you travel in the US?
I had a month of completely uninterrupted photographic time. I flew to Dallas, hired an RV, and drove 3000 miles, through six states. It was quite a simple, monastic way of being - I would get up, have breakfast, unplug my RV, and drive and photograph for about nine or ten hours. Then, depending where I had landed up, I would either camp or find another RV park.
The Hoover Dam, Boulder, Nevada. From the series, America Revisited 2019, © Graeme Williams
Did you finance your trip or is this work commissioned?
Yes, I wanted the freedom to be able to photograph what and how I chose.
What difficulties you had to overcome?
Ned was my only problem. He was the only testing person that I met at the RV parks that I stayed at. He was one of those guys that have no concept of personal space and he was a 'toucher'. After a long day, Ned seemed to be waiting for me, like a stray puppy. Firstly he was determined to direct me into my parking bay, telling me his life story before I had got the reverse angle right and then he kept at it for about half an hour convinced that he was going to persuade me to join him and his wife for a propane barbecue. But apart from Ned, there were no serious challenges.
Did you travel alone?
Yes, passengers would go nuts with my seeming lack of direction and all-consuming interest in the mundane.
People are less present in America Revisited than in Diverging Dreamlines, why?
Yes, that's correct. I wanted to photograph spaces and places that held meaning for me. I didn't purposely avoid including people, but I wanted their presence to be secondary or incidental. I think that we are conditioned to focus on the human element within a frame, but I wanted to communicate how it felt for me to be standing in a particular spot. Of course, the historical imprint of human interaction with any particular space, imbues it with meaning beyond its basic physical form.
Did you have a specific plan in mind of what you wanted to photograph?
When I woke up in the morning, I had no idea what I was going to photograph that day. If I knew what I was going to do, the images wouldn't retain any sense of my presence. It would become more of a technical exercise. The process is a bit like the Eric Clapton song, Running on Faith - you just have to trust that you will see things that spark your interest and then you will know how to photograph them.
Tombstone, Arizona. From the series, America Revisited 2019, © Graeme Williams
Page, Arizona. From the series, America Revisited 2019, © Graeme Williams
What inspires your unique storytelling?
My work is driven by an interest in communicating a feeling, both within the individual images as well as through the body of work as a whole. As photographers, we can become overwhelmed by the collective memory bank of images that has accumulated over two centuries of photography. You have to back up your photographic influences to an external hard drive so you can capture the essence of what one wants to say without too much interference. I think that my continued curiosity about the world and my interest in the potential of the photographic medium, strongly motivate my work.
You explain that after thirty years of photographing South Africa, I felt and still feel a strong need to step off this turbulent rollercoaster that this country personifies for me. Can you elaborate?
There is a sense that South Africans have lived in a state of trauma for centuries. It has always been a violent and harsh environment in which to live and more recently, colonisation and apartheid have left a stain on the psyche of the nation. It is simplistic to think that anyone could remain untouched by this protracted turmoil. For those of us who chose to look closely at the nation's rollercoaster of disorder, trauma has become imprinted in our being. I think that I just felt fatigued by finding myself photographing disturbing subjects that were so similar to those that I witnessed during the apartheid era. At times it seems as if South Africa is a model case study for Sigmund Freud's repetition compulsion.
What are the biggest differences in your opinion between South Africa and the United States? Similarities?
The USA is a machine of efficiency. I am sure that most Americans have very little idea of how their society compares with others around the world. Things really work and most people have jobs. In Southern Africa basic services are uncertain, crime and unemployment are widespread. South Africa, with a population of about 55 million has an average of 58 murders per day, while Zimbabwians live with daily power cuts lasting 17 hours. The USA's complex history and its innate tensions, seem very familiar to me, but as an outsider, I don't find that I get distracted by the micro political shifts.
Bakersfield, Texas. From the series, America Revisited 2019, © Graeme Williams
Do you feel that America changed between 2016 and 2019?
Yes, Donald Trump was fighting for the presidency in 2016 and now he is president. The main difference for me was that this time I didn't have a TV in my RV and I avoided all forms of media. The only political commentary that I saw was on car bumper stickers. The messages seemed to change as I drove westward from Texas to California. During my first trip, I became hooked, watching the televised debates every night in my hotel room. I learnt something from that experience and this time I didn't want my work to wander into the political arena.
If one based one's view of the US purely on media reports, especially social media, it would be reasonable to assume that the USA was in the throes of a second civil war. However, during both of my recent trips, my overriding impression was that Americans displayed a strong sense of respect for the individual, in comparison with people in most other countries that I have visited.
How has your work evolved over the years?
There have been quite distinct phases within South Africa's photographic history. During the apartheid era I was focused on producing work that highlighted the injustice of the system and eventually joined the collective, Afrapix. Then in the late eighties there was a real sense that transformation was possible and imminent. I wanted to be in a position to cover the major political and social changes within the country, and so became a permanent stringer with Reuters News Agency. During the following five years I was immersed in the day-to-day events that led up to the 1994 elections when Nelson Mandela became president. In the mid 90s, we as South African photographers, were confronted by the confluence of a number of major changes: the end of apartheid, a worldwide media shift from reportage towards a celebrity-based focus, digital photography replacing film as well as the art world embracing photography on a more expansive scale. It was a complex process of readjustment after such a long period during which apartheid had been my primary subject matter. I eventually learnt that my real interest is in long-term, very personal essays reflecting my responses to subjects that I am drawn to. This latest shift in focus to the USA is, in a way, an act of freeing myself from my own absorption with the all-consuming subject of South Africa and allowing myself to re-connecting with the essence of what drew me to photography initially; the quest to communicate through photography in an eloquent manner.
The border wall near Yuma, Arizona. From the series, America Revisited 2019, © Graeme Williams
Dallas, Texas. X-marks the spot where JFK was shot. From the series, America Revisited 2019, © Graeme Williams
What equipment do you use?
America Revisited was photographed on a digital Hasselblad, using a variety of lenses and a tilt/shift adapter. My choice of camera depends on what I am trying to achieve. Setting up a heavy tripod and camera, allows one to be far more contemplative about what one allows or removes from a frame.
Why do you work mostly in color?
That is a very relevant question. During apartheid, I would almost exclusively photograph in B/W, because of the unequivocal inequity of the system. While Mandela was president there was a brief period in which most South Africans shared a sense of optimism. My use of color reflects this personal sense of hope, even though the contents of my images were often brutally honest. After Mandela's term as president, this optimism began to be eroded by corruption and poor governance. I found that that in recent years I have again felt that B/W is the best medium through which express my thoughts about South African society. The comparative mood of opportunity and momentum within USA, drew me back to working in color.
What 3 words describe your photography style?
Quiet, lucid and expressive
Las Vegas, Nevada. A view into a Denny's Restaurant on Las Vegas Boulevard. From the series, America Revisited 2019, © Graeme Williams
Tucumcari, New Mexico. From the series, America Revisited 2019, © Graeme Williams
Do you spend a lot of time editing your work?
Yes, I had a month to photograph and when I returned to South Africa, I spent six months to editing, grading and working on the captions. I also collaborated with the former director of Huis Marseille in Amsterdam, Els Barents, to refine the project text so that it was both candid and matched the simplicity of the images.
What advice would you give someone who would like to become a photographer today?
Get a proper job…unless you really have to be a photographer. In which case, trust your instinct and keep going.
What mistake should a young photographer avoid?
Making work that you think might appeal to others.
Your best memory as a photographer?
I think that my most lasting memory was watching Nelson Mandela walk out of prison after 27 years of incarceration. He was truly an amazing man.
What compliment touched you the most?
During my first year as a freelance photographer, I took photographs for the property section of my local newspaper. Even though this was not a very glamorous job, it provided me with access to unlimited amounts of film and enough time to moonlight as a photojournalist. I took a photograph of a white woman comforting a black woman who had been whipped by the apartheid police. The newspaper ran the picture and a few days later I saw the image pinned up in someone's work cubicle. The person told me that the image really moved her and gave her hope. Prior to this, I had never fully understood the act of communicating a feeling through photography and the impact that this process can have on others.
A woman is comforted after being whipped by police during an anti-apartheid demonstration. She was returning to her place of work after doing some shopping when mistaken for a protester by the police. 1986. Cape Town. © Graeme Williams
Your worst souvenir as a photographer?
The realisation that I am not invulnerable, was probably my worst souvenir, but also the insight that helped me to survive some hairy moments. In 1994 a group of right-wing South Africans beat me up and put a shotgun in my mouth, after catching me photographing a colleague of theirs shooting and killing a black woman. Luckily, one of them said to the man holding the shotgun, Don't shoot him, beat him up.' After that incident I lost my sense of invincibility.
What are your upcoming projects?
These images are from the initial phase of this project. I am now looking at ways to extend the coverage to other parts of the United States.
If you weren't a Photographer, what would you be doing?
I studied Geology and Statistics, so I would probably be out on some desolate hill tapping rocks with a geological hammer.
Six Flags Magic Mountain entertainment Park, Santa Clarita, California. From the series, America Revisited 2019, © Graeme Williams
Thank you very much Graeme for taking the time to answer our questions.
We would also like to share with our readers the following passage written by David Goldblatt who was your friend. It was written for PHOTO PAPER in their launch publication used an essay, A city refracted. Kasseler Fotografie Festival, Germany. 2016.
The Spirit of Graeme Williams by David Goldblatt:
'In the discords and harmonies of our life, Graeme Williams has found and shaped his own vision of their existence. He brings the light, shadows, colours, materials, textures, skin, flesh, movement and muscle of our shack settlements and city streets into photographs of dynamic, unexpected, sometimes startling synthesis. He does this with the surging, seemingly effortless fluidity of a dancer. His particular vision was first evidenced, if I am not mistaken, in an extraordinary series of photographs made in 1999 of two black dogs at play with each other on a beach in a flying ballet of explosive energy. There is a straight line of development from that elemental work to the highly complex Edge of Town, photographed between 2007 and 2009 in some 100 of South Africa's 'informal' settlements. Now there is A City Refracted, a more sombre but no less dynamic series of photographs that spring from the tensions of Joburg's streets and the makeshiftedness of living in its unloved and less salubrious buildings. Williams has told me that these essays evolved from the need to transcend the limits of the reportage in which, for many years, he earned his living. But they go far beyond that. They tell of some of his strongly felt understandings of this society. With rare and original imaginative reach, they are eloquently expressive of his spirit.
Twin Arrows Trading Post , Arizona. (Route 66). From the series, America Revisited 2019, © Graeme Williams
North Shore, Saltan Sea, California. From the series, America Revisited 2019, © Graeme Williams
Muscle-Beach, Los Angeles. From the series, America Revisited 2019, © Graeme Williams
Discover Graeme Williams's work on South Africa
Graeme Williams' Website


text:
Every day, Refind picks 5 links that make you smarter. Los Angeles Times's best, and the best from around the web.
Follow Los Angeles Times
Police respond to reports of multiple people shot in Monterey Park
Is the world's richest person the world's worst boss? What it's like working for Elon Musk
These are the 101 best restaurants in Los Angeles
Out of a war zone and into the cloud: Amazon's mission to safeguard critical Ukraine data
Scientists explore using psychedelics to treat alcohol, drug disorders
https://refind.com/latimes


Welcome to Business Internet Providers (ISP) in Grand isle County! This is where we make your job easier when it comes to shopping for Grand isle County Business Internet Service Providers.
Use our Real-Time Grand isle County, Vermont Business ISP quoting tool to find out the best prices on Grand isle County Internet and phone services for businesses of all sizes.
Our technology prices out all types of Internet services from Vermont LEC's, CLEC's, ISP's, and WISP's thoughout all of Grand isle County and beyond!
There is a lot more Grand isle County telecommunications services not mentioned that we have to offer.
Just pick up the phone today and let one of our Grand isle County Telecom Carrier Specialists answer all of your questions.
Receive real-time unbiased Grand isle County, VT Business Internet Service Providers prices from businessinternetprovidersisp.com.
Select the Grand isle County, Business Internet Service Providers price plans that interest you.
A Grand isle Business Internet Service Providers consultant will contact you to discuss the details of the Grand isle County Business Internet Service Providers, confirm pricing, and assist you with the signup process.


The landscape design for this project was an active ecological surface, filtering, cleaning, building and sustaining Talgar and the regional surrounds. Innovative development strategies add a layer of ecological infrastructure that enhance the diversity and richness of the site. The site operates as a responsive habitat, constantly evolving and changing according to the ecological processes and social usage patterns.
This fluid development strategy twines the landscape with development blurring the lines between both. Swaths of open space that protect sensitive natural features, steep slopes and wetlands, allow for fluid movement of both people and nature between site conditions. Considered insertions of residential and commercial development will advantage the spectacular setting and respect the existing terrain while maximizing site development potential. A unique system of physical and visual passages and linkages between the region and the people, the constructed and the natural, the ground and the sky, it allows for free movement from one realm to the other. With few barriers in Talgar, enhanced interactions will contribute to an environmentally responsible, adaptable and efficient development. This strategy will reach beyond the site as Talgar engages adjacent developments and landscapes.
Talgar was designed to be a Loop City with zero waste. In nature, all waste from one system becomes the food for another. Loop City emulates nature's efficiency; independent but interconnected infrastructure systems help reuse waste and reduce pollution while taking care of essential development functions.
CLIENT Multi-functional Administrative City Construction Agency of Korea / PROJECT AREA 2,700,000 m2 / STATUS Competition Finalist, 2007 / DESIGN TEAM Balmori Associates, Inc. / Joel Sanders Architect / MAD office Ltd. / EXE Ltd.
10 Li Park evolves from the overlay and intersection of a central park, a linear park, and architecture. The central park is a space for recreation and experiencing nature, while the linear park "climbs" the nearby mountains, extends onto the river, and weaves through the site to connect the various areas of the immense site. Architectural elements exist at the interface of these two typologies binding them at their most significant intersection. It is a fresh interpretation of each typology that results in new spatial and programmatic strategy for occupying the landscape. The 10 Li Ring combines historical, natural and constructed order of the river, the levee and Public Administration Town (PAT). Li is a traditional Korean unit to measure distance; 10 Li becomes a tool to engage the spatial experiences of the park.
The Ring is a 'Museum Mile' that connects 3 of the planned facilities; a line of culture that creates a porous public boundary between the various landscapes and the architecture. The Li-near Loop is the primary line in the park's succession and growth. All program and park spaces develop out of this loop in time. It is the primary circulation path and an ecological corridor for habitat, filtering, cleaning and purifying air and water; an active environmental engine. In order to maintain a continuous park surface that links to the river and the 10 Li Ring, traffic through the park is placed under this surface before emerging and linking with PAT's road network.
The Performing Arts Center, a catalyst for a large urban revitalization project, is located within the Miami-Dade Empowerment Zone and houses a planned arts, media and entertainment district for Miami's Omni-Venetia area. The Central Plaza for the Arts, designed by Balmori Associates, links the opera house, symphony hall, theatre, and Art Deco tower that sit on either side of the Biscayne Boulevard. This urban plaza bisects Biscayne Boulevard, thereby creating connectivity between the built forms. A wide variety of social and cultural public life is supported by the Plaza.
Furthermore, it can transform from two courts bisected by vehicular traffic into a continuous outdoor plaza for outdoor events when the street is closed. Landscape elements mitigate the changes in elevation, distinguishing elements from each other while creating transitions between others. Rings of plants and fountains at the plaza's edge provide a transition between the street and buildings, which are elevated for purposes of flood protection. The fountain, designed by artist Anna Murch, draws upon wave paths to create a space that is animated even in the absence of water.
In collaboration with Zaha Hadid, Balmori Associates submitted a master plan for the expansion of the University College in Dublin. This design proposed hybridity as a strategy to create new building and landscape typologies. Landscape and architecture merged to form continuous multi-layered public surfaces and green building facades. The slopes that transitioned between the path and the buildings were exemplary of the thickening interface. They were layered with plantings and materials and became usable and occupiable spaces that extend the landscape to a 5th facade of roof garden. This interface also became a sustainable strategy that aimed to maximize campus biodiversity by extending existing green space and branching out to form a new campus green network.
The project at 684 Broadway explores the interface of built and natural environment of architecture and landscape; not blurring the line between landscape and architecture, but widening it. This thick interface creates the opportunity for new types of spaces. Alternating sheaves of landscape and building on both horizontal and vertical planes create transitions within this widened line. It is a complex interface that is layered – the thicker the line the better – and results in a new spatial entity. Interface becomes a sustainable strategy that aims to maximize biodiversity and sustainable design in this urban site by extending green space both horizontally and vertically within the renovated apartment and exterior roof space. The result, hypernature, is an artificial spectacle of constructed nature.
The interface begins with an interior garden beneath a twenty foot long skylight. Filled with large leaved Elephant Ears and black bamboo, the plants create an ascending green carpet beneath the floating stairs to the roof. Above the delicate bamboo fronds, through a glass partition separating the garden from master bathroom, is visible a green wall planted with euonymus. This improbable swath of vertical vegetation climbs the wall colliding with a second skylight through which is visible the rooftop planting.
Suspended above the sea of grasses is a bi-level ipe deck. On the lower level a small gravel path leads to a look out pod with views over the lower east side, an outdoor shower and on the opposite side of the stair bulkhead, a more private enclave with jacuzzi and sunning deck. Five steps lead to the upper level with an outdoor kitchen and grill lounging space. Opposite the parapet, the bulkhead rises into the sky. Densely planted with stepable plants one can lie on the slope and watch cloud rushing overhead. A staircase leads to the top from which there is a 360 degree view of the Lower East side.


When Henry VIII wasn't jousting, playing tennis, shooting his bow and arrow, gambling, at church, smacking Cromwell or chasing the ladies, he was locked away in his chambers mixing up some pretty strange medical cures. Need a cure for those dreaded monthly cramps? Maybe you have a puss-filled ulcer that could use a little TLC? Just head on over to POP Tudors where I will be guest blogging on Henry VIII's favorite cures.


The Chief Commercial Officer (COO) of global crypto payment processor BitPay has ventured that Bitcoin (BTC) will hit $15,000 to $20,000 by the end of 2019. The COO, Sonny Singh, made his forecast during an interview with Bloomberg Nov. 22.
In the midst of a bearish market picture – with Bitcoin down over 32 percent in value on the month – Singh said that he expects the next big price action to come when mainstream financial sector giants such as Fidelity and Intercontinental Exchange (ICE) start to launch their crypto-based investment products next year.
The financial giants' entry into the space could catapult Bitcoin's price to as high as $15,000-$20,000 by the end of 2019, Singh told reporters.
Aside from traditional financial incumbents' launch of crypto-based products, Singh pointed to structural changes in the crypto market itself, with stalwart companies such as U.S. crypto exchange and wallet provider Coinbase and crypto bank Silvergate gearing up for possible initial public offerings (IPOs).
Singh forecast that next year would therefore herald an "exciting" moment: the launch of a crypto-based exchange-traded fund (ETF) by a "Blackrock-type" company or a Fidelity product will energize the space as traditional players jostle for market dominance against "the Bitpays and Coinbases" of the sector.
Remarking that "the ICO market is pretty dead right now," Singh also suggested that signs of increased intervention from the U.S. Securities and Exchange Commission (SEC) does not bode well for the future of the token space.
In an interview this September, Singh outlined a broadly similar argument that the crypto markets are on the threshold of a certain "defining moment," which will come with big institutional investor market entry, set to "become real" in 2019.
Hey Buddy!, I found this information for you: "BitPay COO Sonny Singh: Bitcoin Could Hit -20K by End of 2019". Here is the website link: https://cryptocoingrowth.com/2018/11/23/bitpay-coo-sonny-singh-bitcoin-could-hit-15-20k-by-end-of-2019/. Thank you.


University, Bhopal, Madhya Pradesh, for Elets News Network (ENN).
We are witnessing an ever-growing class of Knowledge Workers who need to update themselves and stay productive at their workplaces. Major proportion of such new class of knowledge aspirants belong to corporate world. Academia has to respond to such increasing demands of lifelong education. It's hardly a matter of choice but an economic compulsion of the knowledge society we are living in.
Situation is challenging for the academia as they have to reach out to work places of the corporate workers and deliver education at the time and place of their choice. Educational Systems are under obligation to adopt flexible ways and means to serve work place requirements and bridge the gap with corporate world. Open and Distance Systems are therefore emerging as the only viable alternative due to their inherently "Flexible and Innovative" nature.
A weak functional relationship between output of educational system and requirements of job market has serious challenge for the economic development. The situation has attracted the renewed attention of policy makers keeping in view the Sustainable Development Goals. Draft New Education Policy of India underlines that weak linkages between University and Industry is one of the reasons for poor research and development. It is increasingly being realized that structured knowledge created in the Universities should blend with the tacit knowledge of the Industrial Workforce. Such a fusion of knowledge and experiences will help to accelerate Industrial growth. On the other hand, it will also help the academia to further explore innovative technologies for increased resource and energy efficiency. To facilitate an effective interface between academia and industry, several policy initiatives have been suggested which includes the provision of having representations from industry in Governing bodies of higher education institutions.
Further, Industry's job multiplication effect has a positive impact on society. It has been estimated that every one job in manufacturing creates 2.2 jobs in other sectors (UNDP web Site). Hence a strong functional dependence between academia and industry is a developmental imperative. A weak academia industry linkage will make industry incapable of supporting other vital sectors of development.
Open and Distance Learning Systems due to their "Innovative and Flexible" character istics are ideally positioned to work in a Multi Stakeholder Environment.It creates a conducive situation for collaborations and networking with industry. Further Open and Distance Learning systems have been biggest users of technology which enhances their capabilities to reach out to working population. Among all the ODL institutions, IGNOU is the major role player which has the technological capability to run Online Knowledge Repository, satellite channels, Network of FM Radio Stations across the country, Network of SIT Terminals for video teleconferencing, A/V Programmes, Mobile E Learning Terminals Vans (MeLT Vans) etc., which favorably position the ODL system to reach out to diverse clientele through ICT enabled methods.
IGNOU is known for its novel approach of collaboration and sharing of resources .University has signed MOUs with several professional bodies, corporate, Government organisations, NGOs, educational institutions, research organisations both in India and abroad to develop Academic Programmes, to create Self Learning Content, develop Multimedia Content, deliver the Programme and Monitor the activities. An innovative project of Hero Honda Ltd., and IGNOU has been widely recognised as the best innovative initiative of University and Corporate organisation. Some of the other prominent organizations which were involved in IGNOU's affairs in the past are the Future Learning and Development Ltd. (FLDL), NIIT Ltd, the Institute of Company Secretaries of India (ICSI), IBM, Bharti Learning Systems Ltd (Centum Learning Ltd), the Cochin International Aviation Service Limited (CIAL), the Institute of Rail Transport (IRT), the Sardar Vallabhbhai Patel International School of Textile & Management (SVPISTM), Global Talent Track (GTT), Training and Advanced Studies in Management & Communication Ltd. (TASMAC), Everonn Education Ltd., Vikas Publishing House Pvt. Ltd., Sri Sanskar School of Etiquette and Career Development, CORE Projects & Technologies Ltd, etc (Source: IGNOU Web Site). The Centre for Corporate Education Training & Consultancy (CCETC) of the University has an interdisciplinary approach to meet the corporate needs. These initiatives of ODL systems in India are some of the success stories.
Corporate Social Responsibility (CSR) has given rise to interesting possibilities of collaboration between Distance Education Institutions and Corporate Houses. The expertise and capabilities of distance education institutions to deliver educational products in remote and far-flung areas can attract the CSR investments. The corporate houses can fund innovative collaborative projects with distance education institutions to enhance their presence in such areas. Whereas Distance Education Institutions will be able to enhance their reach up to hitherto unreached areas, the Corporate Houses will be able to earn brand loyalties in such virgin areas. Such convergence of interests between Distance Education Institutions and Corporate houses need to be fully explored.
Why Demands are So Pressing?
The gaps between academia and industry will have serious consequences for the global pursuits of Sustainable Development Goals. SDG-9 of Post 2015 development agenda of United Nations emphatically highlights the role of Industry. As Industry is one of the core drivers of the Global Economic agenda, any delay to achieve SDG-9 will seriously jeopardize our pursuit to end poverty.
Further, demographic structure of Indian Population have crucial implications for SDGs. The major segment of Indian Population will continue to be young in coming 15-20 years. Moreover India is expected to be the fastest growing economy in the world during this period. Industry and Service sectors are coming up in a big way with expected contribution of 92% of India's GDP by 2030.Report titled "Higher Education in India: Vision 2030" of FICCI Higher Education Summit 2013 highlights that expected growth will require gross incremental workforce of 250 million given retirements / drop outs. Indian Higher Education has a responsibility to supply major share of this work force.
Interestingly, India will have a labor surplus of largely young people in 2030 with a median age of 32 years. These demographic trends have a far reaching impact for SDGs primarily because rest of the world is aging fast. If suitably skilled such young workforce will be able to respond to the massive human resource required to fulfill the demands of labour deficient markets around the world. India has already emerged as a major source of permanent/skilled migrants going to Australia and New Zealand. India's IT/ITeS sector currently employs 2.3 million people who service foreign markets (Reference: FICCI Higher Education Summit 2013). Indian companies are spending increasing amounts on R&D and Government of India is encouraging initiatives to boost R&D in the country. Similarly Global companies are setting up R&D facilities in India. Universities have to play a meaningful role in collaboration with corporate houses to implement such R&D projects. The quality of pass outs of University systems will be crucially important to realise this.
Hence, Indian Higher Education of 21st Centure has to develop as a High Quality, Equitable and Affordable for the young people of the country. Indian Higher Education should be developed as not only best in the world but best for the world. Hence, an effective functional relationship between industry and academia is a developmental imperative which has to face the massive challenge to prepare its young population for the global economy. The effective interface between academia and industry will enhance the employability of its pass-outs , will equip them with the required leadership skills for upcoming industrial needs and respond to continuing professional requirements. Bridging the gaps will help the Industry, Government and Society in different ways. The industry will get benefitted as it will readily get the industry ready talent. Government will get benefitted as industry oriented education will help to reduce the un-employability and enhance the income levels of the people from eligible age group (18- 23 years). At the societal level multiple social benefits will accrue like raised standard of living, more number of jobs getting created. The Global Economy will get obvious advantage as any benefit which will accrue in India for young population will have worldwide impact.


This is a home scent for the white floral lover. This scent is loaded with "exotic" white florals. This fragrant candle is like tropical, heady white floral bomb. It is sweet and slightly spicy for a white floral blend. It fills my house with a spicy tuberose and sweet, humid gardenia. I don't get too much of the fern but this scent is much "cooler" than most tropical floral blends. So, I would say that the fern and lily of the valley are there but I can't pick up on it since the tropical florals are pretty loud. I think those two subdued notes add a watery, humid element. For some reason, this fragrance reminds of Juicy Couture EDP (the "original"). I think because it is a sweet, creamy, humid tropical floral. So to sum this scent up- It's a rich, humid, sweet tropical white floral. It is a heavy scent. I can see how some could find this one overwhelming. I like the scent. I don't crave a scent this humid all of the time, but I do like it occasionally.
I do like the candle. It is very fragrant and it can fragrance my entire house. The candle burns evenly. The scent is throughout the candle. Oh, and the packaging is nice. Many sizes are available. So you can get just a little or a lot of a heavy champaca home scent.
Notes listed include champaca bloom, fresh fern leaf, muguet, and gardenia.
This is a candle to try if you like heavy tuberose and gardenia scents and you want your living space to smell the same as perfumes like Juicy Couture, Estee Lauder Tuberose Gardenia, Urban Rituelle Tahitian Gardenia, Antica Farmacista Ala Moana, Yosh White Flowers, and/or Tom Ford Private Blends Champaca Absolute.
Prices and sizes vary. Voluspa candles are available at Nordstrom.
*Product purchased by me. Product pic from the brand. Post contains an affiliate link. Thanks!
I adore these candles. I give them as gifts…which is kind of cliche', but they are just so fantastic. Everyone loves them!
I would love to get these as a gift! I don't think it is a bad cliche.
The fragrance of this candle is intoxicating!


text:
Home/The Boyle'd Pot/The Boyle'd Pot 25/8/'17
The Boyle'd PotWeekly Blogs
The Boyle'd Pot 25/8/'17
BoyleToday.comAugust 25, 2017
Raids made in relation to local robberies
Armed Gardai conducted a series of dawn raids in Dublin Tuesday last on a "violent" gang suspected for up to 17 robberies in Co Roscommon and neighbouring counties over recent months. It is believed that some of those robberies took place in the general Boyle and North Roscommon area. According to a report on independent.ie "A number of those targeted by Gardaí are understood to have links to slain crime lord 'Fat' Andy Connors – but none of those arrested is related to him." "The extended Connors Traveller gang, which has more than 200 members, was the chief target of Operation Fiacla and other large investigations, but his murder did not end his gang's nationwide crime spree." Read more on this story here
Boyle Show on Sunday
You know the autumn is fast approaching and school term isn't far away when it's Show time around the country. This Sunday it's Boyle's opportunity to celebrate all things rural when the local Show takes place in the GAA training grounds in the Warren. The weather has not been a friend to the show over the year's, and 2017 has been no different with the event quite rightly having been postponed last week due to the wet weather. But the forecast is for better conditions this Sunday. Everyone should make a special effort to attend Boyle Show, an event that is part of the history of the town and area going back many years and one that does not take place without a lot of hard work and behind the scenes planning and organisation.
Two film crews to converge on Boyle
Boyle will once again be a hive of activity this autumn when not one but two TV production crews will film here. The productions are unrelated and will involve two separate crews. While details are not being released yet, it is understood one of the islands in Lough Key will feature prominently in one shoot while Boyle town will feature in a shoot for the other film. It is coincidental that both should pick this autumn to film in our town but the economic benefit of new faces in Boyle at a quiet time of year will hopefully match the publicity the final product will bring to the area. More details on Boyletoday.com in the next few weeks.
Cath Lab in Sligo would be welcomed in Boyle
The news that a business proposal has been completed for a Cardio Cath Lab in Sligo will be welcomed by many locally. Presently those who need urgent treatment for a cardiac arrest have to travel to Galway by road or by air ambulance. There are a number of people in Boyle who owe their life to the air ambulance, which regularly lands in the Abbey Park and transports patients to UCHG in less than one hour. Having the service in Sligo could literally be a life saver for those with cardiac problems in Boyle as time is critical in the event of such an emergency.
N4 needs remedial work conducted
We got away relatively unscathed here in Boyle following last Tuesday evening's torrential downpours. Amazingly, it was one of the busiest national primary roads in the country – the N4 between Boyle and Carrick on Shannon that bore the brunt of the rain in this area with sections of the road near impassable at one stage due to surface water and flooding. That this should occur is a total disgrace considering the majority of the single carriageway is relatively new having been constructed and realigned as part of the Curlew By pass scheme and the Cortober to Meera scheme. Engineers from Transport Ireland need to now look at the road with a view to some remedial action being undertaken to alleviate the retention of surface water. And while they are at it, they should also look at having safety work conducted on the Erris, Knockvicar, Cootehall and Eastersnow turnoffs which are all death traps.
And finally….!
Little Billy Armstrong finally got to tell the teacher what he did during the summer holidays.
"Well Miss" he says "Me and Johnny Jones caught the cat that was digging up our grandads allotment, and we taught it a right good lesson Miss"
" How did you do that" asks Miss.
"Stuck a banger up its bum Miss"
"Rectum" corrected the teacher.
" Aye that's right miss, it blew it ta bits"
Air Corps Boyle horse and summer show N4 rescue 112
Traffic volumes on the increase between Boyle and Carrick
N4 road closure and traffic diversion start today
Further details provided on N4 junction upgrades
Motorists face 14 weeks of delays on N4